diff --git a/spaces/S000169/properties/P000016.md b/spaces/S000169/properties/P000016.md index 544af8656..16debb1ec 100644 --- a/spaces/S000169/properties/P000016.md +++ b/spaces/S000169/properties/P000016.md @@ -4,4 +4,4 @@ property: P000016 value: true --- -This space is a closed and bounded subspace of the Euclidean space $\mathbb{R}^3$. \ No newline at end of file +This space is a closed and bounded subspace of the Euclidean space $\mathbb{R}^3$. diff --git a/spaces/S000169/properties/P000086.md b/spaces/S000169/properties/P000086.md deleted file mode 100644 index e176580ce..000000000 --- a/spaces/S000169/properties/P000086.md +++ /dev/null @@ -1,8 +0,0 @@ ---- -space: S000169 -property: P000086 -value: true ---- - -Any two points on {S169} are related to each other by a rotation of $\mathbb{R}^3$, which restricts to a homeomorphism -of $S^2$. diff --git a/spaces/S000169/properties/P000137.md b/spaces/S000169/properties/P000137.md deleted file mode 100644 index 34d98e8fb..000000000 --- a/spaces/S000169/properties/P000137.md +++ /dev/null @@ -1,7 +0,0 @@ ---- -space: S000169 -property: P000137 -value: false ---- - -By construction. diff --git a/spaces/S000169/properties/P000199.md b/spaces/S000169/properties/P000199.md index a4661ce3b..9982b7757 100644 --- a/spaces/S000169/properties/P000199.md +++ b/spaces/S000169/properties/P000199.md @@ -6,4 +6,5 @@ refs: - zb: "1044.55001" name: Algebraic Topology (Hatcher) --- + This is a consequence of Corollary 2.14 and the statement after Corollary 2.11 of {{zb:1044.55001}}. diff --git a/spaces/S000169/properties/P000240.md b/spaces/S000169/properties/P000240.md index 6a944ff6e..bed4aca6f 100644 --- a/spaces/S000169/properties/P000240.md +++ b/spaces/S000169/properties/P000240.md @@ -14,4 +14,4 @@ The circle can be given a CW complex structure by associating one $0$-cell and o Equivalently, this follows from the fact that CW complexes are preserved under suspensions, and since the sphere is a suspension of {S170}, which is a CW complex {S170|P240}. -See Example 0.3 in {{zb:1044.55001}}. \ No newline at end of file +See Example 0.3 in {{zb:1044.55001}}. diff --git a/spaces/S000170/properties/P000240.md b/spaces/S000170/properties/P000240.md index 65ebad2cb..062b16c77 100644 --- a/spaces/S000170/properties/P000240.md +++ b/spaces/S000170/properties/P000240.md @@ -9,4 +9,4 @@ refs: The circle can be given a CW complex structure by associating one $0$-cell and one $1$-cell: Start with $X_0=\{*\}$, then attach a $1$-cell $D^1 = [-1,1]$ by identifying both boundary points with the $0$-cell (define $f_1: \partial D^1 \to X_0$ by $f_1(\pm 1) = *$.) -See Example 0.3 in {{zb:1044.55001}}. \ No newline at end of file +See Example 0.3 in {{zb:1044.55001}}.